Sampling Theory and the Methods use in foresstry
- 1. 17/03/25 17/03/25 C Dhakal/IAAS C Dhakal/IAAS 1 1 Class 5 Class 5 Sampling Theory and the Sampling Theory and the Methods Methods C Dhakal C Dhakal chudadhakal@gmail.com chudadhakal@gmail.com IAAS IAAS
- 2. 17/03/25 C Dhakal 2 Sample Size Where the frame and population are identical, statistical theory yields exact recommendations on sample size which refers to the number of items to be selected from the universe to constitute a sample
- 3. 17/03/25 C Dhakal 3 Fixing a Sample Size Fixing size of a sample is a major problem to Any researcher • should neither be excessively large nor be too small • should be optimum – an optimum sample is one, which fulfills the requirements of efficiency, representative ness, reliability and flexibility for a given cost
- 4. 17/03/25 C Dhakal 4 Aim of estimating a Sample Size To decrease sampling error to a minimum or an acceptable level. Sampling error is related to the standard error (the standard deviation of the estimates) The standard error (SE) is inversely related to the square root of the sample size.
- 5. 17/03/25 C Dhakal 5 while deciding the size of a sample: • researcher must determine the desired accuracy • and also the acceptable confidence level for the estimate • the allowable error
- 6. 17/03/25 C Dhakal 6 Determination of sample size • Is complex • Involves both practical and statistical factors • Large number of observations is of no value if major sources of variation are neglected in the study • In qualitative research there is more flexibility than in a quantitative research
- 7. 17/03/25 C Dhakal 7 Statistical Factors to consider while determining sample size • Variability in the population • Desired degree of precision (directly proportional) • Desired degree of confidence • The more analysis carried out on subgroups, the larger the sample needed.
- 8. 17/03/25 C Dhakal 8 Practical Factors to consider while determining sample size • Resources available (time, money, personnel) • Expected non-response rates • Expected wear and tear rates • Expected value of information provided by different size samples compared to their costs
- 9. 17/03/25 C Dhakal 9 Foundations for Sample Size Determination 1. Alpha Level 2. Variance Estimation 3. Acceptable Margin of Error
- 10. 17/03/25 C Dhakal 10 Alpha Level • of .05 is acceptable for most researches • is either .05 or .01 for educational research • of .10 or lower may be used if the researcher is more interested in identifying marginal relationships, differences or other statistical phenomena as a pioneer to further studies • of .01 decisions to be taken are critical and errors may cause substantial financial or personal harm
- 11. 17/03/25 C Dhakal 11 Variance Estimation variance estimates must be incorporated into research design (1) take the sample in two steps (2) use pilot study results (discover and solve problem before full implementation) (3) use data from previous studies of the same or a similar population; or (4) estimate or guess the structure of the population assisted by some logical mathematical results. (range rule of thumb)
- 12. 17/03/25 C Dhakal 12 Range Rule of Thumb Where, Range =maximum -minimum 4 ) ( . range deviation d s
- 13. 17/03/25 C Dhakal 13 Acceptable Margin of Error (allowable error) • The maximum likely (with probability ) difference between the observed sample estimate and the true value of population parameter. • Researchers may increase these values when a higher margin of error is acceptable or may decrease these values when a higher degree of precision is needed.
- 14. 17/03/25 C Dhakal 14 Contd. Allowable Error In general, • For categorical data 5% margin of error is acceptable • For continuous data, 3% margin of error is acceptable (of the mean calculated from the research sample).
- 15. 17/03/25 C Dhakal 15 Fixing of Allowable Error confidence of level specified e s statistics parameter . . error allowable statistics parameter
- 16. 17/03/25 C Dhakal 16 Sample Size Determination for Continuous Data Assume that a researcher has set the alpha level a priori at .05, has set the allowable error to be (0.21) and has estimated the standard deviation 1.167. • Cochran’s (1977) sample size formula for continuous data Where, t = value for selected alpha level s=standard deviation and, d= allowable error
- 17. 17/03/25 C Dhakal 17 Cochran’s correction(1977) if a sample size exceeds 5% of the population formula should be used to calculate the final sample size. The formula is given along side For continuous data Where, Where n1 = finale sample size
- 18. 17/03/25 C Dhakal 18 Over Sampling How should one account for lost mail and uncooperative subjects? Answer Do over sampling But How? Answer One way of dealing it is find the ratio of minimal sample size (corrected) to the response rate Hence the formula is as the Followings: Where n2 is adjusted sample size for response rate, n1= minimum sample size (corrected) and r = response rate r n n 1 2
- 19. 17/03/25 C Dhakal 19 four methods may be used to determine the anticipated response rate (1) take the sample in two steps, and use the results of the first step to estimate how many additional responses may be expected from the second step; (2) use pilot study results; (3) use responses rates from previous studies of the same or a similar population; or (4) estimate the response rate.
- 20. 17/03/25 C Dhakal 20 Sample Size Determination for Categorical Data Where t = value for selected alpha level (p) (q) = estimate of variance and (p will be given and q=1-p) d = allowable error
- 21. 17/03/25 C Dhakal 21 Mario F. Triola (1997) Sample Size Formula For estimating population mean (continuous data) • For estimating population proportion (categorical data) 2 2 e n Z 2 2 ) ˆ ˆ ( ) 96 . 1 ( e q p n
- 22. 17/03/25 C Dhakal 22 note: • The existence of such a formula is remarkable because it implies that the sample size does not depend on the size (N) of the population but depends on • desired degree of confidence • the desired margin of error • the value of standard deviation
- 23. 17/03/25 C Dhakal 23 Sample Size Determination Table Table below presents sample size values that will be appropriate for many common sampling problems.
- 24. 17/03/25 C Dhakal 24 Note Situations exist where the procedures described so far will not satisfy the needs of a study. At this other procedures should be adopted.
- 25. 17/03/25 C Dhakal 25 Conclusion Using an adequate sample along with high quality data collection effort will result in more reliable, valid, and generalizable results and possibly in other resource savings too.
- 26. 17/03/25 C Dhakal 26
- 27. 17/03/25 C Dhakal 27 Left Over • Review of sampling process • Non-response • Survey weights • History of sampling
- 28. 17/03/25 C Dhakal 28 A single death is a tragedy; a million deaths is a statistic